Hyperspectral image acquisition system and method

ABSTRACT

A system for acquiring a hyperspectral image, including: a grey level image sensor; and a diffuser and dispersive element placed on the optical path between the sensor and a scene, this element including an array of individually-controllable liquid crystal cells, where each cell can receive a control voltage selected from among a series of at least three different control voltages.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority under 35 U.S.C. §119 of FrenchPatent Application Serial Number 14/54453, filed May 19, 2014, andEuropean Patent Application Serial Number 15168023.8, filed May 19, 2015the disclosures of which are incorporated by reference herein.

BACKGROUND

The present disclosure relates to a hyperspectral or multispectral imageacquisition system and method, and to the calibration of such a systemor method.

Discussion of Related Art

“Hyperspectral or multispectral image of a scene” generally designates aseries of a plurality of elementary images in two dimensions of thescene, each image representing a component of the scene in a restrictedwavelength band. Each elementary image generally corresponds to theintegration of the light intensity in a specific spectral band. In thefollowing, expression “hyperspectral image” is considered as beingequivalent to expression “multispectral image” and designates a seriesof at least two elementary images of a same scene in different spectralbands.

To acquire a hyperspectral image, a method comprises successivelyacquiring the different images of the series by means of an imagesensor, by arranging on each acquisition, between the scene and thesensor, an optical bandpass filter of narrow bandwidth, for example,from a few nanometers to a few tens of nanometers, corresponding to oneof the components of the hyperspectral image. For each new acquisition,a new filter is arranged between the scene and the sensor, tosuccessively select the different spectral bands of the hyperspectralimage.

A major disadvantage of this method is the need to have the differentoptical filters successively pass between the scene and the sensor. Thisresults in relatively bulky acquisition systems and in relatively longacquisition times. Once the acquisition is ended, the informationcontained in each elementary image corresponds to the integration of thelight intensity in the pass-band of the corresponding filter.

Another method comprises using, instead of the filter, a prism, tospatially disperse the different wavelengths of the scene. An arraysystem of programmable shutters, of the type currently called SLM in theart (“Spatial Light Modulator”) may be placed between the scene and theprism, upstream of the image sensor. The SLM is for example formed by anarray of micro-mirrors or by an array of liquid crystal cells. Accordingto the desired spatial and spectral resolutions, an acquisition or asmall number (that is, smaller than the total number of spectral bandsof the hyperspectral image) of acquisitions may be sufficient toreconstruct the hyperspectral image. This type of method is generallycalled CASSI in the art (“Coded Aperture Snapshot Spectral Imaging”).

A disadvantage of this method however is the complexity of the opticalsystem necessary to carry out the acquisition, and the relatively lowresolution of the elementary images which may be simultaneously acquiredby the sensor.

Other methods have been provided, for example, in article “Compressivesensing spectrometry based on liquid crystal devices” of Yitzhak Augustet al., using the theories of compressive acquisition to reconstruct thedifferent components of an extended spectrum based on a small number ofacquisitions. In the above-mentioned article, anelectrically-controllable liquid crystal filter is arranged between thescene and an image sensor. During an acquisition, a control voltage isapplied to the filter, so that the latter, instead of selecting a narrowbandwidth as in conventional methods, selects a wide bandwidth ofirregular shape, corresponding to a juxtaposing of the wavelengths ofthe different components of the hyperspectral image, to which weightingcoefficients are assigned. A plurality of acquisitions are successivelyperformed, by each time modifying the control of the liquid crystalfilter, which amounts to modifying the filter response and thus theweighting coefficients assigned to the components of the hyperspectralimage. The authors have shown that by using the mathematical models ofcompressive acquisition, it is possible to reconstruct a series ofelementary components of the extended spectrum based on a number ofacquisitions smaller than the total number of spectral bands of thereconstructed series.

A disadvantage of this method however is the complexity of thecalibration of the liquid crystal filters, and the limited possibilitiesin terms of compression or of super-resolution.

There is a need for a hyperspectral image acquisition system and methodovercoming all or part of the disadvantages of known solutions.

SUMMARY

Thus, an embodiment provides a system for acquiring a hyperspectralimage, comprising: an image sensor; a diffuser and dispersive elementplaced on the optical path between the sensor and a scene, this elementcomprising an array of liquid crystal cells, each cell beingindividually controllable to vary its refraction index; a control unitcapable of controlling the sensor and the element to successivelyacquire an integral number M greater than 1 of elementary images of thescene, by modifying between two successive acquisitions a set of controlsignals applied to the different cells of the element; and a processingunit capable of reconstructing the hyperspectral image based on the Melementary images acquired by the sensor.

According to an embodiment, for each set of control signals applied tothe element, the element has different point spread functions fordifferent spectral bands of the hyperspectral image.

According to an embodiment, the M sets of control signals applied to thediffuser and dispersive element are such that the acquisition matrix,formed by the concatenation of the representations of the M×K pointspread functions of the element, corresponding to the M applied sets ofcontrol signals and to K spectral bands of the hyperspectral image, Kbeing an integer greater than 1, is of maximum rank relative to itssize.

According to an embodiment, the M sets of control signals applied to thediffuser and dispersive element are such that the M×K point spreadfunctions of the element, corresponding to the M applied sets of controlsignals and to K spectral bands of the hyperspectral image, K being aninteger greater than 1, are all different from one another.

Another embodiment provides a method of controlling the above-mentionedsystem, comprising an acquisition phase during which the sensor and theelement are controlled to successively acquire an integral number Mgreater than 1 of elementary images of the scene, by modifying betweentwo successive acquisitions the set of control signals applied to thedifferent cells of the element.

According to an embodiment, the control method further comprises a phaseof reconstructing the hyperspectral image based on the M elementaryimages acquired during the acquisition phase.

According to an embodiment, the control method further comprises aprevious calibration phase during which the M×K point spread functionsof the element, corresponding to the M sets of applied control signalsand to K spectral bands of the hyperspectral image, K being an integergreater than 1, are determined.

According to an embodiment, the calibration phase comprises theacquisition successively by the sensor of M×K images of spots resultingfrom the diffusion, by the element, for the M sets of control signals ofthe element and for the K light spectral bands of the hyperspectralimage, of a point light source having a settable wavelength or having aknown and settable spectral signature.

According to an embodiment, the M×K images acquired during thecalibration phase are matched with a theoretical behavior model of theelement.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other features and advantages will be discussed indetail in the following non-limiting description of specific embodimentsin connection with the accompanying drawings, in which:

FIG. 1 schematically and partially shows an embodiment of ahyperspectral image acquisition system;

FIG. 2 is a diagram illustrating the operating principle of thehyperspectral image acquisition system of FIG. 1; and

FIG. 3 schematically and partially shows the hyperspectral imageacquisition system of FIG. 1 during a calibration phase.

DETAILED DESCRIPTION

For clarity, the same elements have been designated with the samereference numerals in the different drawings.

FIG. 1 schematically and partially shows an embodiment of ahyperspectral image acquisition system.

The system of FIG. 1 comprises an image sensor 101, for example, anarray of photodetectors, capable of providing images in grey levels.Image sensor 101 is a wide-band sensor, that is, it is sensitive to allthe wavelengths of the hyperspectral images which are desired to beacquired.

The system of FIG. 1 further comprises, on the optical path betweensensor 101 and an object or a scene 103 (OBJ) for which a hyperspectralimage is desired to be acquired, a programmable diffuser and dispersiveelement 105, comprising an array of liquid crystal cells individuallycontrollable to vary their refraction indexes. The liquid crystals ofelement 105 are liquid crystals having a refraction index depending onthe wavelength, and preferably liquid crystals having their wavelengthdispersion varying according to the applied bias voltage, for example,liquid crystals of the type commercialized by MERCK under referenceTL216 or under reference E44. As a non-limiting example, each elementarycell may have dimensions in the range from 1 to 10 μm for applicationsin the visible range. In practice, element 105 may comprise a continuousliquid crystal layer having a first surface coated with a continuouscommon electrode and having a second surface opposite to the firstsurface covered with an array network of individually-controllablediscrete elementary electrodes. In this case, an elementary cell ofelement 105 is formed by the portion of the liquid crystal layerarranged between an elementary electrode and the common electrode.

In this example, object 103 for which a hyperspectral image is desiredto be acquired is assumed to be located at infinity. Possibly, acomplementary optical system, not shown, may be arranged between theobject and element 105 so that object 103 appears at infinity from theviewpoint of element 105.

The system of FIG. 1 may further comprise one or a plurality of memories(not shown) capable of storing one or a plurality of digital imagesacquired by sensor 101, a calculation unit (not shown), for example, amicroprocessor, capable of processing images acquired by sensor 101,and/or a control unit of sensor 101 and of diffuser and dispersiveelement 105.

The operation of the system of FIG. 1 will now be described.

During a phase of acquisition of a hyperspectral image of object 103,sensor 101 successively acquires M images y_(m) of object 103 seenthrough diffuser and dispersive element 105, where M is an integergreater than 1 and m is an integer in the range from 1 to M.

On acquisition of an image y_(m), diffuser and dispersive element 105 ismodulated by a set of control signals C_(m), that is, a set of signalsfor controlling the different liquid crystal cells of element 105. Eachset of control signals enables to generate a specific map of refractionindexes on the liquid crystal array. In the described embodiments,instead of being controlled to be shut/opened as in a SLM of aCASSI-type system, each cell may receive a control voltage selected froma series of at least three different voltages, and preferably from aseries of at least ten different voltages, corresponding to at leastthree, respectively to at least ten, different refraction indexes (for agiven wavelength). Preferably, element 105 is such that, for a givencontrol signal set C_(m) of element 105, there is no refraction indexdiscontinuity at the border between two adjacent cells of the array, sothat the liquid crystal layer of element 105 is perceived as anon-discrete element (that is, continuous or analog). The M sets ofcontrol signals C_(m) applied to element 105 during the M imageacquisitions by sensor 105 are all different from one another. For eachset of control signals Cm of element 105, element 105 has a point spreadfunction PSF which varies according to the wavelength of the raysreceived by element 105 (dispersive character of element 105). For agiven set of control signals C_(m) of element 105 and for a givenwavelength, the PSF of element 105 forms a diffusion spot, preferablyuneven, capable of spreading over a plurality of photodetectors ofsensor 101 and preferably over the most part of the surface of sensor101 (diffusing character of element 105). Defining the PSF of element105, for a given wavelength, with the image of the spot, in the plane ofsensor 101, resulting from the diffusion by element 105 of a beamoriginating from a point light source at this wavelength, sets Cm ofcontrol signals are preferably selected so that the M×K PSFs of element105 (K being an integer greater than 1 corresponding to the number ofspectral bands of the hyperspectral image which is desired to beacquired) are sufficiently decorrelated from one another. As an example,a group of M sets of control signals of element 105 may be selected fromamong a group of sets of control signals generated based on Zernikepolynomials to minimize the intercorrelation maximum and theautocorrelation maximum of the PSFs. As an example, a group of sets ofcontrol signals adapted for a given wavelength may be selected, afterwhich a bias capable of minimizing the correlation of the PSFs on thespectral axis may be determined for each set of control signals in thegroup. Preferably, for a given set of control signals, the spectraldeviation of the PSF between two successive spectral bands of thehyperspectral image to be acquired is smaller than or equal to a pixelof the sensor, to avoid certain spectral artifacts. In terms ofcompressive acquisition, it may further be desired to minimize themutual coherence between the acquisition matrix (relative to the PSFs)and the base where the hyperspectral images which are desired to beacquired are parsimonious. Further, to define sets of control signalsenabling to generate orthogonal PSFs for a given wavelength, anon-negative principal component analysis of a group of PSFs generatedfrom sets of control signals originating from Zernike polynomials may beperformed. It is then possible to return to the sets of control signalsassociated with the orthogonal PSFs by means of an algorithm enabling torecover the wavefronts corresponding to the generated PSFs.

Sets C_(m) of control signals are preferably selected so that, for agiven set of control signals C_(m) and for a given wavelength, the PSFof element 105 is substantially the same at any point of element 105. Inother words, sets C_(m) of control signals are preferably selected sothat, for a given set of control signals C_(m) and for a givenwavelength, the image resulting from the object in the plane of sensor101 corresponds to the convolution of the image of the object by aconvolution kernel corresponding to the PSF associated with theconsidered set of control signals C_(m) and with the consideredwavelength. If such is not the case, a correction of the distortion maybe incorporated to the hyperspectral image reconstruction algorithm. Itshould be noted that such a distortion may depend on several parameters,including the discretization of dispersive element 105, its size and itsshape, as well as the possible influence of its temperature gradient. Itwill be within the abilities of those skilled in the art to adapt theused secondary optical systems to minimize their impacts in terms ofdistortion while taking into account the influence of element 105.

For each set of control signals C_(m) of element 105, different liquidcrystal cells of element 105 are controlled to have different refractionindexes (for each wavelength) to create phase shifts of the wavefront atthe output of element 105 (and more generally at the output of thegeneral optical system comprising element 105), enabling to generateuneven diffusion spots or PSFs. As an example, sets C_(m) of controlsignals correspond to sets of control signals enabling to generate knownPSFs, for example, PSFs originating from aberrations of the wavefrontcorresponding to Zernike polynomials or to a combination of suchpolynomials. The case of astigmatism aberrations or of sphericalaberrations coupled with a bias or tilt should in particular be noted asa non-limiting example.

As will be explained in further detail hereafter, the inventors havedetermined that based on the M fuzzy images y_(m) acquired by sensor 101during the acquisition phase, it is possible to restore a hyperspectralimage x comprising K elementary images x_(λk) corresponding to thecomponents of image x in the different spectral bands λ_(k) of image x(k being an integer in the range from 1 to K). The calculations enablingto reconstruct hyperspectral image x based on the M images y_(m) will bedetailed hereafter. Such calculations may be implemented either by meansof a calculation unit integrated to the acquisition system, or by anexternal processing unit.

A sufficient discretization of hyperspectral image x along the axis ofthe different spectral bands will be assumed hereafter, so that the stepof this discretization is small as compared with the variations of thespectral signatures observable on each pixel. Number M of images y_(m)necessary to reconstruct spectral image x depends on the parsimony ofimage x in a given representation base (that is, on its structuralcomplexity), on its spatial and spectral resolution, and on thecoherence of the acquisition matrix equivalent to the convolutionsperformed by the different PSFs (the stronger the correlation betweenthe different PSFs, the higher the number of images y_(m) necessary forthe reconstruction of image x).

h_(m),λ_(k), designates the convolution kernel corresponding to theeffect of the PSF of element 105 on the light of spectral band λk, whenelement 105 receives set of control signals C_(m). Considering that thedesired elementary images x_(λk) have a resolution P×Q greater by afactor s than resolution Ps×Qs of sensor 101, with P, Q, s, P_(s), andQ_(s) being integers, P_(s)=P/s and Q_(s)=Q/s, and considering that theM×K PSFs of element 105 may be defined with a granularity level ordiscretization step identical to that of images x_(λk), each image y_(m)acquired by sensor 101 may be analytically expressed with the followingformula:

${y_{m} = {D_{s}\left( {\sum\limits_{k = 1}^{K}{h_{m,{\lambda \; k}}*x_{\lambda \; k}}} \right)}},$

where * represents the convolution operator (non cyclic), and whereD_(s) designates an operator of decimation by factor s, for example, anaveraging operator, corresponding to the spatial decimation, by sensor101, of hyperspectral image x. FIG. 2 shows a simplified modelization ofthis equation.

It is first considered that a hyperspectral image x at the same spatialresolution P_(s)×Q_(s) as sensor 101 is desired to be obtained, and thatthe M×K PSFs of element 105 can be defined with a granularity levelcorresponding to resolution P_(s)×Q_(s) of the sensor. Operator D_(s)can thus be omitted (case s=1). Convolution operations in the spatialdomain correspond to point-by-point multiplications or Hadamard productsin the Fourier domain. The above-mentioned equation can then beapproximated as follows:

${Y_{m} = {\sum\limits_{k = 1}^{K}{H_{m,{\lambda \; k}} \cdot X_{\lambda \; k}}}},$

where ‘.’ represents the Hadamard product, Y_(m) is the Fouriertransform of image y_(m), H_(m,λk) is the Fourier transform ofconvolution kernel h_(m,λk) (possibly completed with zeros if thedimensions of kernel h_(m,λk) are smaller than the dimensions of imagex_(λk)), and X_(λk) is the Fourier transform of elementary image x_(λk).It should be noted that edge effects may, if need be, be compensated byusing methods of zero-padding type, that is, by increasing the size ofthe matrixes and by completing them with zeros.

For each pixel of spatial coordinates p,q of hyperspectral image x,where p is an integer in the range from 1 to P and q is an integer inthe range from 1 to Q, this equation may be expressed in the form of asimple matrix multiplication, as follows:

Y(p,q)=G(p, q)X(p, q),

where Y(p,q) is a vector of dimension M, containing the M values of thepixel of coordinates p,q in the M Fourier transform images Ym, X(p,q) isa vector of dimension K containing the K values of the pixel ofcoordinates p,q in the K Fourier transform images Xλk, and G(p,q) is amatrix of dimensions M×K containing the M×K values of the pixels ofcoordinates p,q in the M×K Fourier transforms H_(m,λk) of convolutionkernels h_(m,λk).

The case where number M of acquisitions performed by sensor 101 is equalto number K of elementary images of the desired hyperspectral image x isconsidered. Matrixes G(p,q) then are square matrixes. If the M×K PSFs ofelement 105 are sufficiently decorrelated from one another, squarematrixes G(p,q) may be inverted or pseudo-inverted. The M sets C_(m) ofcontrol signals of element 105 are preferably selected so that squarematrixes G(p,q) are invertible. Each vector X(p,q) of the Fouriertransform hyperspectral image may be directly calculated by a simplematrix multiplication according to the following formula:

X(p,q)=G(p,q,)⁻¹ Y(p,q),

where G(p,q)−1 designates inverted or pseudo-inverted matrix G(p,q). Thedifferent elementary images x_(λk) of hyperspectral image x can then bereconstructed by simple inverse Fourier transform operations.

More generally, be matrix G(p,q) square or not, the M sets of controlsignals C_(m) of element 105 are preferably selected so that theacquisition matrix, formed by the concatenation of the representationsof the different PSFs in the spatial and spectral fields, is of maximumrank relative to its size. The size of the acquisition matrix is definedfor its number of rows, that is, the number of acquired data, and itsnumber of columns, that is, the number of data which are desired to bereconstructed.

An advantage of the above-described hyperspectral image acquisitionsystem is that it is particularly simple and of low bulk. In particular,it is not necessary to provide a mechanism enabling to mechanicallychange the optical filter located between the sensor and the scenebetween the different acquisitions. Further, the forming of element 105is relatively simple since element 105 should not perform an accurateconventional optical filtering function, but only introduce fuzzinessinto the image, the only constraint being for the M×K PSFs of element105 to have a good level of decorrelation relative to one another.

It should be noted that matrixes G(p,q)⁻¹ may be predetermined, andstored in a memory of a hyperspectral image reconstruction unit.Matrixes G(p,q)⁻¹ may further optionally be preconditioned to avoidcertain errors due to edge effects.

More generally, if the number of pixel values effectively acquired issmaller than the number of pixel values to be reconstructed, forexample, if number M of acquisitions performed by sensor 101 is smallerthan number K of elementary images of the hyperspectral image x which isdesired to be reconstructed, and/or if spatial resolution P×Q ofhyperspectral image x is greater than resolution pxq of sensor 101 (cases>1), image x may be reconstructed by means of an iterativeregularization method of the type used in compressive acquisition,corresponding to the resolution of a minimization problem formulated asfollows:

${\arg \; {\min_{x}\left( {{J(x)} + {\gamma {\sum\limits_{m = 1}^{M}{{{D_{s}{\sum\limits_{k = 1}^{K}{h_{m,{\lambda \; k}}*x_{\lambda \; k}}}} - y_{m}}}_{2}^{2}}}} \right)}},$

where J(x) corresponds to a regularization operator enabling toexacerbate the internal structure of the hyperspectral image and γ is ascalar regularization parameter. As a non-limiting example, operatorJ(x) is based on five gradient operators ∇₁, ∇₂, ∇₃, ∇₄, and ∇₅,corresponding to constraints which apply to the cube of dimensions P×Q×Kof hyperspectral image x, respectively in the vertical (P), horizontal(H), and diagonal directions of space, and in the spectral direction(K), expressed as follows:

$\left( {\nabla_{1}x} \right)_{p,q,k} = \left\{ {{\begin{matrix}{{x_{{p + 1},q,k} - x_{p,q,k}},} & {{p < P},} \\{0,} & {{p = P},}\end{matrix}\left( {\nabla_{2}x} \right)_{p,q,k}} = \left\{ {{\begin{matrix}{{x_{p,{q + 1},k} - x_{p,q,k}},} & {{q < Q},} \\{0,} & {{q = Q},}\end{matrix}\left( {\nabla_{3}x} \right)_{p,q,k}} = \left\{ {{\begin{matrix}{{x_{{p + 1},{q + 1},k} - x_{p,q,k}},} & {{p < {P\bigcap q} < Q},} \\{0,} & {{p = {{P\bigcup q} = Q}},}\end{matrix}\left( {\nabla_{4}x} \right)_{p,q,k}} = \left\{ {{\begin{matrix}{x_{{p + 1},{q - 1},k},x_{p,q,k},} & {{p < {P\bigcap q} > 1},} \\{0,} & {{p = {{P\bigcup q} = 1}},}\end{matrix}\left( {\nabla_{5}x} \right)_{p,q,k}} = \left\{ \begin{matrix}{{x_{p,q,{k + 1}} - x_{p,q,k}},} & {{k < K},} \\{0,} & {{k = K},}\end{matrix} \right.} \right.} \right.} \right.} \right.$

Operator J(x) may for example be defined by the following formula:

${{J(x)} = {{{\Psi \; {\nabla_{5}x}}}_{1} + {\sum\limits_{i = 1}^{4}{{\nabla_{i}x}}_{1}}}},$

where Ψ designates a selected bidimensional wavelet transform operator.

As a variation, operator J(x) may take other forms. For example,operator J(x) may be an operator enabling, by using the so-callednuclear standard, to minimize the number of different spectralsignatures in the reconstructed data.

Further, rather than reconstructing the complete hyperspectral image(one intensity value per pixel and per spectral band), it may beprovided to reconstruct data directly usable by the consideredapplication, for example, a map of materials, or indications relative tothe presence or not of certain phenomena or objects in the hyperspectralimage.

An advantage of the provided acquisition system and method is that theyenable to acquire hyperspectral images having a spatial resolutiongreater than that of the sensor and/or having a number of differentspectral bands greater than the number of acquisitions performed by thesensor, in a particularly simple way. In particular, the acquisition ofa hyperspectral image having a resolution greater than that of thesensor can be performed by a system comprising neither prism, nocoded-aperture matrix shutter device.

Another major advantage is that, during the acquisition, no spectralfiltering is performed, which implies that the selection of thereconstructed bands does not depend on the acquisition, but only resultsfrom a choice made at the time of the reconstruction. It is thuspossible, based on a same series of M images y_(m) of a scene acquiredby sensor 101, to select the number and the position of thereconstructed bands. A compromise should of course often be made betweenthe size of the spectral bands, their number, the spatial resolution ofthe reconstructed image, and the quality/reliability of thereconstructed image.

Whatever the method selected to reconstruct hyperspectral image x basedon the M images y_(m) acquired by sensor 101, it is necessary to knowthe different PSFs h_(m,λk) of element 105. PSFs h_(m,λk) may forexample be determined during a system calibration phase, or bedetermined by simulation based on theoretical models of response ofelement 105, or also be determined by a method combining calibration andsimulation.

FIG. 3 schematically and partially illustrates the hyperspectral imageacquisition system of FIG. 1 during a calibration phase enabling todetermine the different PSFs hm,_(λk) of element 105.

In this example, object 103 of FIG. 1 is replaced with a point lightsource 303 having a settable wavelength, enabling to successively scanthe K spectral bands λ_(k) of the hyperspectral images which are desiredto be acquired. Source 303 for example is a laser source having asettable wavelength. As a variation, source 303 may comprise a wide-bandsource coupled to a plurality of optical bandpass filters capable ofbeing individually activated, corresponding to the different spectralbands of the hyperspectral images which are desired to be acquired.

During a calibration phase, it may first be provided to apply set C₁ ofcontrol signals to element 105 and to control source 303 to only emit inspectral band λ₁. An image can then be acquired by sensor 101, definingPSF h₁,λ₁ of element 105 for set C₁ of control signals and forwavelength λ₁. The operation may be repeated K times without modifyingthe set of control signals of element 105 but by each time modifying theemission wavelength of the source, to go through the K spectral bands ofthe hyperspectral images which are desired to be acquired. The entireoperation can then be repeated M times by each time modifying the set ofcontrol signals applied to element 105 to use the M controls C_(m)capable of being applied to element 105 and thus obtain the M×K PSFsh_(m,λk) of element 105.

This method enables to obtain PSFs h_(m,λk) having a granularity levelor discretization step identical to that of sensor 101, and having anoise level corresponding to that of the sensor. It may however beadvantageous to define PSFs h_(m,λk) with a discretization step smallerthan that of the sensor and/or with a noise level lower than that of thesensor (particularly if a hyperspectral image having a spatialresolution greater than that of the sensor or having a number ofelementary images x_(λk) greater than the number of images y_(m)acquired by the sensor is desired to be reconstructed). To achieve this,the PSFs may be determined by simulation, by means of a theoreticalbehavior model of element 105.

Another particularly advantageous method for determining PSFs h_(m,λk),combining calibration and simulation, will now be described.

To begin with, M×K images hs_(m,λk) corresponding to the M×K PSFs ofelement 105 at the resolution of sensor 101, may be acquired by using asource of a settable wavelength according to the above-mentionedcalibration method. It is then provided to pool the informationcollected during this acquisition phase to decrease the noise andpossibly increase the resolution of the acquired PSFs.

For each band of wavelengths λ_(k) of the hyperspectral images which aredesired to be acquired, a theoretical behavior model h_(λk)(Ω) may bedefined, where Ω designates a set of a limited number of parameters ofelement 105. Theoretical model h_(λk)(Ω) may for example have adiscretization step smaller than that of sensor 101.

For each set of control signals C_(m) of element 105, the performedmeasurements hs_(m,λk) are put in correspondence with theoreticalbehavior model h_(λk) to determine a set of parameters Ω_(m) definingthe real behavior of element 105 for set C_(m) of control signals. SetΩ_(m) may be determined by means of an error minimization algorithm, forexample, an iterative algorithm, solving the following minimizationproblem (in the case where the effect of a Gaussian-type noise isdesired to be decreased):

${\Omega_{m} = {\arg \; {\min_{\Omega}\left( {{C(\Omega)} + {\gamma {\sum\limits_{k = 1}^{K}{{{hs}_{m,{\lambda \; k}} - {D_{s}{h_{\lambda \; k}(\Omega)}}}}_{2}^{2}}}} \right)}}},$

where D_(s) is a decimation operator corresponding to the averagingperformed by sensor 101 during the acquisition, with respect to an imagehaving the same resolution as theoretical model h_(λk), where γ is ascalar regularization parameter, and where C(Ω) is an operator ofconstraints on a set of parameters Ω.

Each of the M×K PSFs h_(m,λk) of element 105 can then be determined bythe following formula:

h _(m,λk) =h _(λk)(Ω_(m)).

This enables to take into account possible imperfections of theacquisition system which cannot be modeled by means of theoreticalpreconceptions. Advantageously, an interpolation and smoothing functionI may be applied. PSFs h_(m,λk) of element 105 can then be determined bythe following formula:

h _(m,λk) =h _(λk)(Ω_(m))−I _(s)(hs _(m,λk) −D _(s) h _(λk)(Ω_(m)).

Specific embodiments have been described. Various alterations,modifications, and improvements will readily occur to those skilled inthe art.

In particular, a new solution enabling to acquire hyperspectral imageshas been provided. Based on the above-described teachings, it will bewithin the abilities of those skilled in the art to adapt certainaspects of the described method and system according to the targetedapplication. For example, although only embodiments where diffuser anddispersive element 105 operates in transmission mode have been shown inthe drawings, the described embodiments are not limited to this specificcase. Thus, an acquisition system of the type described in relation withFIGS. 1 to 3, where element 105 operates in reflection mode, may beprovided.

1. A system for acquiring a hyperspectral image, comprising: an imagesensor; a diffusion and dispersive element placed on the optical pathbetween the sensor and a scene, this element comprising an array ofliquid crystal cells, each cell being individually controllable to varyits refraction index; a control unit capable of controlling the sensorand the element to successively acquire an integral number M greaterthan 1 of elementary images of the scene, by modifying between twosuccessive acquisitions a set of control signals applied to thedifferent cells of the element; and a processing unit capable ofreconstructing the hyperspectral image based on the M elementary imagesacquired by the sensor.
 2. The system of claim 1, wherein, for each setof control signals applied to the element, the element has differentpoint spread functions for different spectral bands of the hyperspectralimage.
 3. The system of claim 2, wherein the M sets of control signalsapplied to the diffuser and dispersive element are such that theacquisition matrix, formed by the concatenation of the representationsof the M×K point spread functions of the element, corresponding to the Mapplied sets of control signals and to K spectral bands of thehyperspectral image, K being an integer greater than 1, is of maximumrank relative to its size.
 4. The system of claim 2, wherein the M setsof control signals applied to the diffuser and dispersive element aresuch that the MK point spread functions of the element corresponding tothe M applied sets of control signals and to K spectral bands of thehyperspectral image, K being an integer greater than 1, are alldifferent from one another.
 5. A method of controlling the system ofclaim 1, comprising an acquisition phase during which the sensor and theelement are controlled to successively acquire an integral number Mgreater than 1 of elementary images of the scene, by modifying betweentwo successive acquisitions the set of control signals applied to thedifferent cells of the element.
 6. The method of claim 5, furthercomprising a phase of reconstructing the hyperspectral image from the Melementary images acquired during the acquisition phase.
 7. The methodof claim 5, further comprising a previous calibration phase during whichthe M×K point spread functions of the element, corresponding to the Mapplied sets of control signals and to K spectral bands of thehyperspectral image, K being an integer greater than 1, are determined.8. The method of claim 7, wherein the calibration phase comprises theacquisition successively by the sensor of M×K images of spots resultingfrom the diffusion, by the element, for the M sets of control signals ofthe element and for the K light spectral bands of the hyperspectralimage, of a point light source having a settable wavelength.
 9. Themethod of claim 8, wherein the M×K images acquired during thecalibration phase are matched with a theoretical behavior model of theelement.
 10. A method of controlling the system of claim 2, comprisingan acquisition phase during which the sensor and the element arecontrolled to successively acquire an integral number M greater than 1of elementary images of the scene, by modifying between two successiveacquisitions the set of control signals applied to the different cellsof the element.
 11. A method of controlling the system of claim 3,comprising an acquisition phase during which the sensor and the elementare controlled to successively acquire an integral number M greater than1 of elementary images of the scene, by modifying between two successiveacquisitions the set of control signals applied to the different cellsof the element.
 12. A method of controlling the system of claim 4,comprising an acquisition phase during which the sensor and the elementare controlled to successively acquire an integral number M greater than1 of elementary images of the scene, by modifying between two successiveacquisitions the set of control signals applied to the different cellsof the element.
 13. The method of claim 10, further comprising a phaseof reconstructing the hyperspectral image from the M elementary imagesacquired during the acquisition phase.
 14. The method of claim 11,further comprising a phase of reconstructing the hyperspectral imagefrom the M elementary images acquired during the acquisition phase. 15.The method of claim 12, further comprising a phase of reconstructing thehyperspectral image from the M elementary images acquired during theacquisition phase.
 16. (Previously Presented as second claim 14) Themethod of claim 10, further comprising a previous calibration phaseduring which the M×K point spread functions of the element,corresponding to the M applied sets of control signals and to K spectralbands of the hyperspectral image, K being an integer greater than 1, aredetermined.
 17. The method of claim 11, further comprising a previouscalibration phase during which the M×K point spread functions of theelement, corresponding to the M applied sets of control signals and to Kspectral bands of the hyperspectral image, K being an integer greaterthan 1, are determined.
 18. The method of claim 12, further comprising aprevious calibration phase during which the M×K point spread functionsof the element, corresponding to the M applied sets of control signalsand to K spectral bands of the hyperspectral image, K being an integergreater than 1, are determined.
 19. The method of claim 10, furthercomprising a phase of reconstructing the hyperspectral image from the Melementary images acquired during the acquisition phase.
 20. The methodof claim 11, further comprising a phase of reconstructing thehyperspectral image from the M elementary images acquired during theacquisition phase.